Electrical transmission lines are used in a variety of applications, such as carrying communication signals between spaced-apart locations. In some applications, the transmission lines are used as delay lines to induce delay in electrical signals. For example, U.S. patent application Serial No. 08/019,774 of Gold et al., and assigned to OWL Display, Inc., discloses a tapped microwave transmission line using coincident pulses to control a matrix addressable display.
Often, the delay line must be very long to produce adequate delays. For example, the propagation-delay time per unit length for a microstrip line in a non-magnetic medium is T.sub.d =1.016.sqroot..epsilon., ns/ft where .epsilon..sub.r is a relative dielectric constant of the substrate, as described in Liao, "Microwave Devices and Circuits," 2d Ed., Prentice Hall, Inc., 1985. For a relative dielectric constant .epsilon..sub.r, of 2.0, the propagation-delay time per unit length is 1.437 ns/ft. Thus, for a 100 ns delay, the line would be approximately 69.6 ft. Unfortunately, such long lengths of transmission line are extremely large and lossy making such lines undesirably for many applications.
To address such drawbacks, much work has been directed toward decreasing the propagation velocity V.sub.P of signals in transmission lines because the propagation delay T.sub.d of a signal in a transmission line is inversely proportional to the propagation velocity V.sub.P. The propagation velocity V.sub.P for a transmission line is inversely proportional to the square-root of the effective dielectric constant .epsilon..sub.e times the effective permeability .mu..sub.e. Thus, the propagation velocity is ##EQU1## and the propagation-delay time per unit length T.sub.d is T.sub.d =.sqroot..mu..sub.e .epsilon..sub.e .
The effective permeability .mu..sub.e and the effective dielectric constant .epsilon..sub.e are determined by the transmission line geometry, the relative permeabilities .mu..sub.r of the materials, and the relative dielectric constants .epsilon..sub.r of the materials. The propagation velocity V.sub.P thus increases as a function of the relative dielectric constants .epsilon..sub.r and the relative permeabilities .mu..sub.r of the materials.
Previous attempts to reduce propagation velocities V.sub.P in transmission lines have focused primarily upon the dielectric medium because increases in the relative dielectric constant .epsilon..sub.r of the dielectric medium increase the effective dielectric constant .epsilon..sub.e and thereby decrease the propagation velocity V.sub.P along the transmission line. For example, for microstrip lines, a variety of substrate materials having extremely large relative dielectric constants .epsilon..sub.r have been suggested. Such increases are limited by the availability and cost of high relative dielectric constant materials.
To further reduce propagation velocity, the relative permeability .mu..sub.r of the substrate material and/or the surrounding regions can also be increased. Such increases in relative permeability .mu..sub.r of the substrate or surrounding regions increases the effective permeability .mu..sub.e of the transmission line, thereby decreasing propagation velocity V.sub.P. However, such increases are limited by relative permeabilities of available materials, physical constraints of the transmission line structure and losses of the available materials.
Such constraints can be particularly problematic in small transmission lines, such as microstrip lines in matrix addressable displays. In such displays, spacing between adjacent columns is very small to allow relatively high resolution. Consequently, if the microstrip lines extend between successive columns of the display, the time delay between arrival of pulses of successive columns is very small. To increase the timing separation between adjacent columns, the microstrip line can be formed in a serpentine pattern. However, this approach is limited by the physical constraints of the display and the losses of the serpentine microstrip line. Consequently, additional reductions in the propagation velocity V.sub.P remain desirable.